The sum of two numbers is $31$, and their difference is $1$. What are the two numbers?
Answer: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 31}$ ${x-y = 1}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 32 $ $ x = \dfrac{32}{2} $ ${x = 16}$ Now that you know ${x = 16}$ , plug it back into $ {x+y = 31}$ to find $y$ ${(16)}{ + y = 31}$ ${y = 15}$ You can also plug ${x = 16}$ into $ {x-y = 1}$ and get the same answer for $y$ ${(16)}{ - y = 1}$ ${y = 15}$ Therefore, the larger number is $16$, and the smaller number is $15$.